Optimal. Leaf size=92 \[ -\frac {81}{64} (1-2 x)^{15/2}+\frac {81}{4} (1-2 x)^{13/2}-\frac {97335}{704} (1-2 x)^{11/2}+\frac {4165}{8} (1-2 x)^{9/2}-\frac {74235}{64} (1-2 x)^{7/2}+\frac {12005}{8} (1-2 x)^{5/2}-\frac {184877}{192} (1-2 x)^{3/2} \]
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Rubi [A] time = 0.02, antiderivative size = 92, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.045, Rules used = {77} \[ -\frac {81}{64} (1-2 x)^{15/2}+\frac {81}{4} (1-2 x)^{13/2}-\frac {97335}{704} (1-2 x)^{11/2}+\frac {4165}{8} (1-2 x)^{9/2}-\frac {74235}{64} (1-2 x)^{7/2}+\frac {12005}{8} (1-2 x)^{5/2}-\frac {184877}{192} (1-2 x)^{3/2} \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin {align*} \int \sqrt {1-2 x} (2+3 x)^5 (3+5 x) \, dx &=\int \left (\frac {184877}{64} \sqrt {1-2 x}-\frac {60025}{8} (1-2 x)^{3/2}+\frac {519645}{64} (1-2 x)^{5/2}-\frac {37485}{8} (1-2 x)^{7/2}+\frac {97335}{64} (1-2 x)^{9/2}-\frac {1053}{4} (1-2 x)^{11/2}+\frac {1215}{64} (1-2 x)^{13/2}\right ) \, dx\\ &=-\frac {184877}{192} (1-2 x)^{3/2}+\frac {12005}{8} (1-2 x)^{5/2}-\frac {74235}{64} (1-2 x)^{7/2}+\frac {4165}{8} (1-2 x)^{9/2}-\frac {97335}{704} (1-2 x)^{11/2}+\frac {81}{4} (1-2 x)^{13/2}-\frac {81}{64} (1-2 x)^{15/2}\\ \end {align*}
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Mathematica [A] time = 0.02, size = 43, normalized size = 0.47 \[ -\frac {1}{33} (1-2 x)^{3/2} \left (2673 x^6+13365 x^5+29565 x^4+38220 x^3+32220 x^2+18696 x+7288\right ) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.59, size = 44, normalized size = 0.48 \[ \frac {1}{33} \, {\left (5346 \, x^{7} + 24057 \, x^{6} + 45765 \, x^{5} + 46875 \, x^{4} + 26220 \, x^{3} + 5172 \, x^{2} - 4120 \, x - 7288\right )} \sqrt {-2 \, x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.20, size = 106, normalized size = 1.15 \[ \frac {81}{64} \, {\left (2 \, x - 1\right )}^{7} \sqrt {-2 \, x + 1} + \frac {81}{4} \, {\left (2 \, x - 1\right )}^{6} \sqrt {-2 \, x + 1} + \frac {97335}{704} \, {\left (2 \, x - 1\right )}^{5} \sqrt {-2 \, x + 1} + \frac {4165}{8} \, {\left (2 \, x - 1\right )}^{4} \sqrt {-2 \, x + 1} + \frac {74235}{64} \, {\left (2 \, x - 1\right )}^{3} \sqrt {-2 \, x + 1} + \frac {12005}{8} \, {\left (2 \, x - 1\right )}^{2} \sqrt {-2 \, x + 1} - \frac {184877}{192} \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 40, normalized size = 0.43 \[ -\frac {\left (2673 x^{6}+13365 x^{5}+29565 x^{4}+38220 x^{3}+32220 x^{2}+18696 x +7288\right ) \left (-2 x +1\right )^{\frac {3}{2}}}{33} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.49, size = 64, normalized size = 0.70 \[ -\frac {81}{64} \, {\left (-2 \, x + 1\right )}^{\frac {15}{2}} + \frac {81}{4} \, {\left (-2 \, x + 1\right )}^{\frac {13}{2}} - \frac {97335}{704} \, {\left (-2 \, x + 1\right )}^{\frac {11}{2}} + \frac {4165}{8} \, {\left (-2 \, x + 1\right )}^{\frac {9}{2}} - \frac {74235}{64} \, {\left (-2 \, x + 1\right )}^{\frac {7}{2}} + \frac {12005}{8} \, {\left (-2 \, x + 1\right )}^{\frac {5}{2}} - \frac {184877}{192} \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 64, normalized size = 0.70 \[ \frac {12005\,{\left (1-2\,x\right )}^{5/2}}{8}-\frac {184877\,{\left (1-2\,x\right )}^{3/2}}{192}-\frac {74235\,{\left (1-2\,x\right )}^{7/2}}{64}+\frac {4165\,{\left (1-2\,x\right )}^{9/2}}{8}-\frac {97335\,{\left (1-2\,x\right )}^{11/2}}{704}+\frac {81\,{\left (1-2\,x\right )}^{13/2}}{4}-\frac {81\,{\left (1-2\,x\right )}^{15/2}}{64} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 3.22, size = 82, normalized size = 0.89 \[ - \frac {81 \left (1 - 2 x\right )^{\frac {15}{2}}}{64} + \frac {81 \left (1 - 2 x\right )^{\frac {13}{2}}}{4} - \frac {97335 \left (1 - 2 x\right )^{\frac {11}{2}}}{704} + \frac {4165 \left (1 - 2 x\right )^{\frac {9}{2}}}{8} - \frac {74235 \left (1 - 2 x\right )^{\frac {7}{2}}}{64} + \frac {12005 \left (1 - 2 x\right )^{\frac {5}{2}}}{8} - \frac {184877 \left (1 - 2 x\right )^{\frac {3}{2}}}{192} \]
Verification of antiderivative is not currently implemented for this CAS.
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